Some witches are "psychics", Psionic. Especially Nordic witches.
Some witches are shamanic, Psionic, such as various animistic cultures, including shamans and witchdoctors and medicinefolk
Some witches are fay. Especially, Scot witches from the Renaissance and earlier, who interacted with the Elf queen and were often healers. Psionic or Primal or Arcane (In D&D the source for the Feywild is ambiguous.)
Some witches are theistic, Divine, such as Greek Hecate.
Some witches are devilish, Divine or Arcane, such as certain grimoire descriptions from continental Europe.
Some witches are protoscientific, Arcane or Primal, or Divine in the sense of cosmic force such as elementalism, such as Celtic traditions of Druid and Bard potion making, or Roman Period Hellenistic "magi" amuletic use of plants and gems.
Probably, the most important question is whether they themself is the power source internally, such as psychic or a family of psychics, or something else is the power source externally, such as harnessing the magical properties that are inherent in different kinds of plants and gems, or gaining the assistance of a spirit who does tasks.
If it was just power source (like arcane pacts, or divine blessings, or primal spirit mediating, or elemental channelling) I still think it would be fine to consider it a single class.
But Witches are also different in their approach to the nature of magic.
I can think of two classes that scream Witch especially in how they reach out to different power sources:
Warlock just needs to add a few more pacts like The Primal Spirit, The Divine Pairing, The Elements.
Sorcerer is almost good as it is, but could use an explicitly Fey origin, and perhaps a Cosmic Magic source (as well as Frost Sorcery, Flame Sorcery, and Stone Sorcery for more elemental themes beyond Storm Sorcery).
But again, there's Artificers that feel very much in line with historical Euro-American Witches as alchemists and healers that were demonized by a rising male industry of medicine; there's Bards who lean into the ecstatic and performative side of witchcraft and healing, while also being dabblers and seers - there's a reason that Troubadours, Nuns, Witches, & Concubines share a history of countercurrent creation in medieval Eurasia. And there's Druids and Wizards who have each inherited much of the tropes of witchcraft we have in popular fiction today. And of course there's always Clerics and Monks; the lines between witch and faith practitioner is often a line drawn by oppressors. Or, the rising dominant religious communities recasts magical persons as religious ones; Goddesses become Saints or Angels, Witches become Nuns or Priestesses reinforcing the divine right of the heroes they interacted with.
Look at Morgan le Fay from the Arthurian cycles. She's been cast as a witch, a sorceress, a depraved nun, a misunderstood priestess of an old religion, a misunderstood nun or priestess of the current religion, a goddess taking human form, a demigod, a fairy queen, or a female magus of some kind with powers similar to Merlin (himself a character that has been expressed in a multitude of ways and could be represented by the D&D Wizard, Bard, Sorcerer, Warlock, Cleric, Artificer, or even Fighter or Paladin or Ranger if we're talking Emrys or Ambrosius).
Magic in stories don't necessarily comply with each other. Maybe it's an argument for combining magical classes and calling it all just Mage with different flavours, but I think 5e resolves this best of any D&D edition: it's able to provide us with tools to enact classic character archetypes and then to finetooth it with subclasses. The answer thus would be to give us 5 different Witches that all have different flavours of Witch and sit within different classes, or to find the witchiest of witch ideas and make it a Strixhaven-style subclass that thus can combine with various classes to form the best idea of what a witch is to a given player. But doing so would also require guidance to figuring out the systems mastery, and I recognise that some people just want to be a witch and be done with it (much like some want to be a champion fighter and be done with options paralysis). In that case, I would want chapter 1 or 2 guidance directing them to classic archetypal characters, and witch could be one of them, saying if you want to play a witch of that classical variety, choose the Warlock class, etc.